Designing Off-axis Optical System With Freeform Reflective And Diffractive Surfaces By A Modified Seed Curve Extension Algorithm

Off-axis freeform imaging optical systems have a wide range of applications,such as hyperspectral imaging spectrometers,extreme ultraviolet lithography objectives,and space telescopes.For off-axis freeform imaging optical systems,it is very important to explore the design method of the initial structure.The seed curve extension(SCE)algorithm can directly design the initial structure of the off-axis freeform system,but this algorithm has certain limitations:(1)it cannot design the freeform diffractive surface,(2)it is difficult to design an off-axis imaging system with limited object distance.In this paper,a multifunctional seed curve extension(MSCE)algorithm is developed,which can design not only freeform reflective surfaces but also freeform diffractive surfaces.In addition,MSCE algorithm has no restrictions on the object distance of off-axis imaging systems.This paper also designs the orthogonal seed curve extension(OSCE)algorithm,which can reduce the tendency of the normal vector error to gradually increase in the process of constructing the freeform surface of the SCE algorithm.In order to verify the effectiveness of the algorithm,off-axis reflective imaging systems,off-axis reflective afocal systems and an imaging spectrometer including a freeform diffractive grating are designed.The research contents of this thesis are divided into three parts:(1)An off-axis freeform four-mirror imaging system is designed by using the seed curve extension(SCE)algorithm.According to the initial conditions,using the law of reflection and the constraints between adjacent sampling points,the iterative relationship between adjacent sampling points can be constructed.Based on this iterative relationship,all sampling points on the seed curve can be obtained,and then the seed curve is extended to obtain the sampling points on the entire freeform surface.Taking the reflected light of the first freeform surface as the incident light of the second freeform surface,and repeating the above process,the sampling points on the second freeform surface can be obtained.The initial structure of the off-axis four-mirror system is designed by using the SCE algorithm.The F-number of the four-mirror system is 2 and the full field of view is 5°.The MTF value of the initial structure of the system designed by the seed curve extension algorithm is 0.5 at 20lps/mm.After optimization,the MTF value of full field of view of the system is above 0.75,which is close to the diffraction limit.(2)The orthogonal seed curve extension(OSCE)algorithm is developed.The curve in this algorithm is extended along two orthogonal directions,which can effectively reduce error of constructing surface in the process of the curves extension.In order to compare the optical performance of the initial layouts designed by SCE and OSCE algorithms,three types of off-axis freeform reflective afocal systems were designed by the SCE and OSCE algorithms,respectively with the same initial conditions.It is shown that the RMS wavefront error of the layout of the off-axis fourmirror and three-mirror afocal systems designed by the OSCE algorithm are reduced by a factor of 4and 2,respectively,compared with the SCE algorithm.Also,the initial layouts of an off-axis threemirror afocal systems consisting of two channels are designed by OSCE algorithm.After optimization,the RMS wavefront error of each channel in the two-channel system is about 0.04λ.(3)A multifunctional seed curve extension(MSCE)algorithm is developed,which can construct freeform reflective or diffractive surface directly.By employing the MSCE algorithm,the layouts of three types of spectrometers are designed.The first spectrometer consists of a plane grating and three freeform mirrors,with object and image points on both sides of the grating.The second spectrometer consists of a plane grating,two freeform mirrors and one plane mirror,with object and image points on the same side of the grating.The spectral range of the two spectrometers are 400-800 nm.With initial layouts designed by MSCE algorithm,the two systems are further optimized.The MTF values of the two systems at 20 lps/mm and 30 lps/mm are 0.7 and 0.6,respectively.The third spectrometer is an Offner type spectrometer,which includes a freeform grating and two freeform mirrors.The initial layout is designed by the MSCE algorithm at the wavelength of 700 nm.And the RMS radius of the spot diagram of the initial layout is about 14 μm.The initial layout is taken as a starting point for the subsequent optimization.After optimization,the MTF value of the system is above 0.77 at 30 lps /mm within the wavelength range of 400-1000 nm.A tolerance analysis is performed on the third spectrometer using Monte Carlo analysis method.Within the given tolerance range,MTF values of90% of samples are greater than 0.4 at 30 lps /mm.